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Title:
Szabo’s Geometric Spectral Sequence for Tangles
Speaker:
Abstract:
Szabo recently wrote down (seemingly out of nowhere) a combinatorial chain complex associated to a link diagram L in S^3, modeled on Khovanov homology, which conjecturally computes the Heegaard Floer homology of the branched double cover of S^3 along L. In this talk, I’ll describe an extension of Szabo’s work to tangles, modeled on Khovanov’s “functor-valued invariant of tangles.” I’ll introduce A-infinity algebras and modules and describe how to compute Szabo’s invariant of a link L by decomposing L into tangles and computing the invariants of these simpler objects (our pairing theorem). At the end, I’ll mention a striking relationship (coincidental?) between the structures apparent in this tangle theory and a version of the Fukaya category of the once-punctured torus explored by Lekili and Perutz. This talk will be fairly basic and should provide intuition for the more complicated construction I’ll describe in the Topology Seminar. This is joint work with Cotton Seed.
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